# Properties

 Label 280.2.q Level $280$ Weight $2$ Character orbit 280.q Rep. character $\chi_{280}(81,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $16$ Newform subspaces $5$ Sturm bound $96$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$280 = 2^{3} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 280.q (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$5$$ Sturm bound: $$96$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(280, [\chi])$$.

Total New Old
Modular forms 112 16 96
Cusp forms 80 16 64
Eisenstein series 32 0 32

## Trace form

 $$16 q + 4 q^{3} - 2 q^{5} + 4 q^{7} - 6 q^{9} + O(q^{10})$$ $$16 q + 4 q^{3} - 2 q^{5} + 4 q^{7} - 6 q^{9} + 2 q^{11} + 16 q^{13} - 4 q^{17} - 2 q^{19} - 6 q^{21} - 8 q^{25} - 32 q^{27} + 4 q^{29} - 16 q^{31} - 2 q^{35} + 4 q^{37} + 20 q^{39} + 8 q^{41} + 48 q^{43} - 12 q^{45} + 12 q^{47} - 2 q^{49} + 4 q^{51} - 4 q^{53} + 8 q^{57} - 4 q^{59} + 2 q^{61} - 12 q^{63} - 6 q^{65} - 12 q^{67} + 4 q^{69} - 48 q^{71} - 12 q^{73} + 4 q^{75} - 48 q^{77} - 8 q^{79} - 16 q^{81} - 88 q^{83} - 44 q^{87} + 14 q^{89} + 12 q^{91} - 44 q^{93} - 4 q^{95} - 16 q^{97} + 92 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(280, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
280.2.q.a $2$ $2.236$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$1$$ $$-5$$ $$q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots$$
280.2.q.b $2$ $2.236$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$1$$ $$1$$ $$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots$$
280.2.q.c $2$ $2.236$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$1$$ $$4$$ $$q+(2-2\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots$$
280.2.q.d $4$ $2.236$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$2$$ $$-2$$ $$-2$$ $$q+(1+\beta _{1}+\beta _{2})q^{3}+\beta _{2}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots$$
280.2.q.e $6$ $2.236$ 6.0.11337408.1 None $$0$$ $$0$$ $$-3$$ $$6$$ $$q-\beta _{5}q^{3}+(-1+\beta _{2})q^{5}+(1-\beta _{1}-\beta _{5})q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(280, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(280, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(35, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(70, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(140, [\chi])$$$$^{\oplus 2}$$